Exact solution for the layered convection of a viscous incompressible fluid at specified temperature gradients and tangential forces on the free boundary

Abstract

A new exact analytical solution of a system of thermal convection equations in the Boussinesq approximation describing layered flows in an incompressible viscous fluid is obtained. A fluid flow in an infinite layer is considered. Convection in the fluid is induced by tangential stresses specified on the upper non-deformable boundary. At the fixed lower boundary, the no-slip condition is satisfied. Temperature corrections are given on the both boundaries of the fluid layer. The possibility of physical field stratification is investigated. © 2017 Author(s).